Finite Group Databasebeta

← C3×#79648 #11860558

Subgroups — C3×#79648 #11860558

Order 1152.

1001 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#915C211yesmaximal, characteristic
2C3×#5572C211yesmaximal, characteristic, complemented
3C3×#5546C211yesmaximal, characteristic
4C32×C4×SD16C211yesmaximal, characteristic, complemented
5C3×#5164C211yesmaximal, characteristic, complemented
6C3×#5030C211yesmaximal, characteristic, complemented
7C3×#5018C211yesmaximal, characteristic, complemented
8C3×#4861C211yesmaximal, characteristic, complemented
9C3×#4853C211yesmaximal, characteristic, complemented
10C3×D3×#103C211yesmaximal, characteristic, complemented
11C3×#4790C211yesmaximal, characteristic, complemented
12C3×#4772C211yesmaximal, characteristic
13C3×#4758C211yesmaximal, characteristic, complemented
14C3×C4×Dic12C211yesmaximal, characteristic, complemented
15C3×#4689C211yesmaximal, characteristic, complemented
16C3×#2947—31nomaximal
17#79648C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic
22C32×C4×D4C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic
26C2×C3×#214C2211yescharacteristic
27C3×C4×#67—21no—
28C2×C3×Dic3⋊C4—21no—
29C3×#915C418yescomplemented
30C2×C3×Dic12C2211yescharacteristic
31C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
32C2×C3×D3×C8C2211yescharacteristic
33C3×#892—21no—
34C3×#892C2211yescharacteristic
35C3×D3×C4⋊C4C2211yescharacteristic
36C3×#887—21no—
37C3×#887C2211yescharacteristic
38C3×#887C2211yescharacteristic
39C3×#67⋊C4—21no—
40C3×#877—21no—
41C3×#872—21no—
42C3×#872C2211yescharacteristic
43C3×C4×Dic6—21no—
44C3×C4×Dic6C2211yescharacteristic
45C3×C4×Dic6C2211yescharacteristic
46C32×#106C2211yescharacteristic
47C32×#103C2211yescharacteristic
48C32×#102C2211yescharacteristic
49C32×C4×C8C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#832C2211yescharacteristic
52C3×#818C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#816C2211yescharacteristic
55C3×#815C2211yescharacteristic
56C3×C8×Dic3C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#810C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#807C2211yescharacteristic
61C3×#803C2211yescharacteristic
62C2×C3×#137—31no—
63C3×#520—31no—
64C3×#519—31no—
65C2×#915C2×C311yescharacteristic
66#5572C2×C311yescharacteristic, complemented
67#5546C2×C311yescharacteristic
68C3×#441—31no—
69C3×#441—31no—
70C3×#440—31no—
71C3×#440—31no—
72C3×C4×Q16—31no—
73C3×C4×Q16—31no—
74C3×C4×SD16—21no—
75C3×C4×SD16—31no—
76C3×C4×SD16D311yescharacteristic, complemented
77C3×C4×SD16C2×C311yescharacteristic, complemented
78C3×#428—31no—
79C3×#416—31no—
80C2×C3×#103—31no—
81C3×#405—31no—
82#5164C2×C311yescharacteristic, complemented
83#5030C2×C311yescharacteristic, complemented
84#5018C2×C311yescharacteristic, complemented
85#4861C2×C311yescharacteristic, complemented
86#4853C2×C311yescharacteristic, complemented
87D3×#103C2×C311yescharacteristic, complemented
88#4790C2×C311yescharacteristic, complemented
89#4772C2×C311yescharacteristic
90#4758C2×C311yescharacteristic, complemented
91C4×Dic12C2×C311yescharacteristic, complemented
92#4689C2×C311yescharacteristic, complemented
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4—21no—
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C22×C3×Dic3—21no—
99C3×D3×Q8—22no—
100C3×D3×Q8C2×C414yescomplemented
101C3×#237—22no—
102C3×#237C2×C414yes—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6—21no—
107C2×C3×Dic6C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C32×SD16C2×C414yescomplemented
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116C32×C42—21no—
117C32×C42C2311yescharacteristic
118C3×#217—21no—
119C3×#216C2×C414yescomplemented
120C3×#214C2×C414yescomplemented
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4D411yescharacteristic
133C3×Dic3⋊C4D411yescharacteristic
134C3×C4×Dic3—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3—21no—
138C3×C4×Dic3—21no—
139C3×C4×Dic3—21no—
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×Dic12C2×C414yescomplemented
144C3×ΓL(1,𝔽25)C2×C414yescomplemented
145C3×D3×C8—22no—
146#2947—31noSylow
147C2×C3×#41—31no—
148C22×C3×Q8—31no—
149C2×D3×Q8C22×C311yescharacteristic
150C2×#237C22×C311yescharacteristic
151C3×#137—38no—
152C2×C3×Q16—31no—
153C2×C3×Q16—31no—
154C2×C3×SD16—21no—
155C2×C3×SD16—31no—
156C2×C3×SD16C2×D311yescharacteristic
157C2×C3×SD16C22×C311yescharacteristic
158C2×C3×M16—31no—
159C22×C3×C8—31no—
160C3×C4×Q8—21no—
161C3×C4×Q8—31no—
162C3×C4×Q8—31no—
163C3×C4×Q8—31no—
164C3×C4×Q8—31no—
165C3×C4×Q8—31no—
166C3×C4×Q8—61no—
167C3×C4×Q8—61no—
168C3×C4×Q8C2×D311yescharacteristic
169C3×C4×Q8C22×C311yescharacteristic
170C3×C4×D4—21no—
171C3×C4×D4—31no—
172C3×C4×D4—61no—
173C3×C4×D4—61no—
174C3×C4×D4C2×D311yescharacteristic
175C3×C4×D4C22×C311yescharacteristic
176C3×#117—31no—
177C3×#117—31no—
178C3×#117—61no—
179C3×#117—61no—
180C3×#117—61no—
181C2×C3×C4⋊C4—31no—
182C2×C3×C4⋊C4—61no—
183Q8×Dic3C22×C311yescharacteristic
184C2×#216C22×C311yescharacteristic
185D4×Dic3C22×C311yescharacteristic
186C2×#214C22×C311yescharacteristic
187C4×#67—21no—
188C2×Dic3⋊C4—21no—
189#915C3×C418yescomplemented
190C2×Dic12C22×C311yescharacteristic
191C2×ΓL(1,𝔽25)C22×C311yescharacteristic
192C2×D3×C8C22×C311yescharacteristic
193#892—21no—
194#892C22×C311yescharacteristic
195D3×C4⋊C4C22×C311yescharacteristic
196#887—21no—
197#887C22×C311yescharacteristic
198#887C22×C311yescharacteristic
199#67⋊C4—21no—
200#877—21no—
201#872—21no—
202#872C22×C311yescharacteristic
203C4×Dic6—21no—
204C4×Dic6C22×C311yescharacteristic
205C4×Dic6C22×C311yescharacteristic
206C3×#107—31no—
207C3×#107—31no—
208C3×#106—21no—
209C3×#106—31no—
210C3×#106C2×D311yescharacteristic
211C3×#106C22×C311yescharacteristic
212C3×#103—21no—
213C3×#103—31no—
214C3×#103—31no—
215C3×#103—31no—
216C3×#103—31no—
217C3×#103—31no—
218C3×#103C2×D311yescharacteristic
219C3×#103C22×C311yescharacteristic
220C3×#102—21no—
221C3×#102—31no—
222C3×#102C2×D311yescharacteristic
223C3×#102C22×C311yescharacteristic
224C3×#97—31no—
225C3×#97—31no—
226C3×C4×C8—21no—
227C3×C4×C8—31no—
228C3×C4×C8C2×D311yescharacteristic
229C3×C4×C8C22×C311yescharacteristic
230#835C22×C311yescharacteristic
231#832C22×C311yescharacteristic
232#818C22×C311yescharacteristic
233#816C22×C311yescharacteristic
234#816C22×C311yescharacteristic
235#815C22×C311yescharacteristic
236C8×Dic3C22×C311yescharacteristic
237#810C22×C311yescharacteristic
238#810C22×C311yescharacteristic
239#808C22×C311yescharacteristic
240#807C22×C311yescharacteristic
241#803C22×C311yescharacteristic
242C23×C32—21no—
243C22×C3×D3C2×D411yescharacteristic
244C32×Q8—21no—
245C32×Q8C22×C412yes—
246C32×D4—21no—
247C32×D4C22×C412yes—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—81no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2411yescharacteristic
255C3×#67—24no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—24no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—81no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×C4×D3—24no—
266C3×C4×D3—81no—
267C3×C4×D3C22×C412yes—
268C3×C4×D3#4112yes—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—24no—
272C3×Dic6C22×C412yes—
273C3×Dic6C22×C412yes—
274C32×C8—21no—
275C32×C8C22×C412yes—
276C3×C3⋊C8—21no—
277C3×C3⋊C8C22×C412yes—
278C2×#137—31no—
279#520—31no—
280#519—31no—
281#441—31no—
282#441—31no—
283#440—31no—
284#440—31no—
285C4×Q16—31no—
286C4×Q16—31no—
287C4×SD16—31no—
288C4×SD16C3×D311yescharacteristic, complemented
289#428—31no—
290#416—31no—
291C2×#103—31no—
292#405—31no—
293C3×#41—34no—
294C3×#41—62no—
295C2×C3×Q8—21no—
296C2×C3×Q8—34no—
297C2×C3×Q8—31no—
298C2×C3×Q8—31no—
299C2×C3×Q8—61no—
300C2×C3×Q8—62no—
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C23×C311yescharacteristic
303C2×C3×D4—21no—
304C2×C3×D4—61no—
305C2×C3×D4C22×D311yescharacteristic
306C2×C3×D4C23×C311yescharacteristic
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—31no—
310C22×C3×C4—41no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C2×#67—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318D3×Q8—22no—
319D3×Q8C2×C3×C414yescomplemented
320#237—22no—
321#237C2×C3×C414yes—
322C2×C4×D3—21no—
323C2×C4×D3—21no—
324C2×C4×D3C23×C311yescharacteristic
325C2×Dic6—21no—
326C2×Dic6C23×C311yescharacteristic
327C2×Dic6C23×C311yescharacteristic
328C3×Q16—34no—
329C3×Q16—34no—
330C3×SD16—24no—
331C3×SD16—34no—
332C3×SD16C4×D314yescomplemented
333C3×SD16C2×C3×C414yescomplemented
334C3×M16—34no—
335C2×C3×C8—21no—
336C2×C3×C8—21no—
337C2×C3×C8—31no—
338C2×C3×C8—31no—
339C2×C3×C8—62no—
340C2×C3×C8C22×D311yescharacteristic
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C23×C311yescharacteristic
343C2×C3×C8C23×C311yescharacteristic
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—41no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C4⋊C4C23×C311yescharacteristic
362C3×C4⋊C4C23×C311yescharacteristic
363C3×C22⋊C4—21no—
364C3×C22⋊C4—21no—
365C3×C22⋊C4—31no—
366C3×C22⋊C4—31no—
367C3×C22⋊C4—41no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C42—21no—
371C3×C42—21no—
372C3×C42—21no—
373C3×C42—31no—
374C3×C42—41no—
375C3×C42—61no—
376C3×C42—61no—
377C3×C42—61no—
378C3×C42—61no—
379C3×C42—61no—
380C3×C42—61no—
381C3×C42C22×D311yescharacteristic
382C3×C42C23×C311yescharacteristic
383#217—21no—
384#216C2×C3×C414yescomplemented
385#214C2×C3×C414yescomplemented
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4C3×D411yescharacteristic
388(C2×D3)⋊C4C3×D411yescharacteristic
389C4⋊Dic3—21no—
390C4⋊Dic3C23×C311yescharacteristic
391C4⋊Dic3C23×C311yescharacteristic
392Dic3⋊C4—21no—
393Dic3⋊C4—21no—
394Dic3⋊C4—21no—
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397Dic3⋊C4C3×D411yescharacteristic
398Dic3⋊C4C3×D411yescharacteristic
399C4×Dic3—21no—
400C4×Dic3—21no—
401C4×Dic3—21no—
402C4×Dic3—21no—
403C4×Dic3—21no—
404C4×Dic3—21no—
405C4×Dic3C23×C311yescharacteristic
406C2×C3⋊C8C23×C311yescharacteristic
407C2×C3⋊C8C23×C311yescharacteristic
408Dic12C2×C3×C414yescomplemented
409ΓL(1,𝔽25)C2×C3×C414yescomplemented
410D3×C8—22no—
411C22×C32—22no—
412C22×C32—41no—
413C22×C32—41no—
414C22×C32C22×D411yescharacteristic
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3C4×D412yes—
418C32×C4—21no—
419C32×C4—22no—
420C32×C4—21no—
421C32×C4—41no—
422C32×C4—41no—
423C32×C4C23×C411yescharacteristic
424C32×C4C2×#4111yescharacteristic
425C3×Dic3—22no—
426C3×Dic3—22no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3C4×D412yes—
432C2×#41—31no—
433C22×Q8—31no—
434#137—38no—
435C2×Q16—31no—
436C2×Q16—31no—
437C2×SD16—31no—
438C2×SD16C2×C3×D311yescharacteristic
439C2×M16—31no—
440C22×C8—31no—
441C4×Q8—31no—
442C4×Q8—31no—
443C4×Q8—31no—
444C4×Q8—31no—
445C4×Q8—31no—
446C4×Q8—61no—
447C4×Q8—61no—
448C4×Q8C2×C3×D311yescharacteristic
449C4×D4—31no—
450C4×D4—61no—
451C4×D4—61no—
452C4×D4C2×C3×D311yescharacteristic
453#117—31no—
454#117—31no—
455#117—61no—
456#117—61no—
457#117—61no—
458C2×C4⋊C4—31no—
459C2×C4⋊C4—61no—
460#107—31no—
461#107—31no—
462#106—31no—
463#106C2×C3×D311yescharacteristic
464#103—31no—
465#103—31no—
466#103—31no—
467#103—31no—
468#103—31no—
469#103C2×C3×D311yescharacteristic
470#102—31no—
471#102C2×C3×D311yescharacteristic
472#97—31no—
473#97—31no—
474C4×C8—31no—
475C4×C8C2×C3×D311yescharacteristic
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—31no—
479C23×C3—41no—
480C22×D3C2×C3×D411yescharacteristic
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—22no—
484C3×Q8—32no—
485C3×Q8—32no—
486C3×Q8—41no—
487C3×Q8—64no—
488C3×Q8—61no—
489C3×Q8—61no—
490C3×Q8C2×C4×D312yes—
491C3×Q8C22×C3×C412yes—
492C3×D4—21no—
493C3×D4—21no—
494C3×D4—22no—
495C3×D4—41no—
496C3×D4—64no—
497C3×D4C2×C4×D312yes—
498C3×D4C22×C3×C412yes—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—31no—
509C2×C3×C4—32no—
510C2×C3×C4—32no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—64no—
517C2×C3×C4—64no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—81no—
523C2×C3×C4—81no—
524C2×C3×C4—82no—
525C2×C3×C4—241no—
526C2×C3×C4—241no—
527C2×C3×C4D3×D411yescharacteristic
528C2×C3×C4D3×D411yescharacteristic
529C2×C3×C4C2×C3×D411yescharacteristic
530C2×C3×C4C2×C3×D411yescharacteristic
531C2×C3×C4C23×D311yescharacteristic
532C2×C3×C4C24×C311yescharacteristic
533#67—24no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—24no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—81no—
540C2×Dic3C2×C3×D411yescharacteristic
541C2×Dic3C2×C3×D411yescharacteristic
542C2×Dic3C2×C3×D411yescharacteristic
543C4×D3—24no—
544C4×D3—81no—
545C4×D3C22×C3×C412yes—
546C4×D3C3×#4112yes—
547Dic6—21no—
548Dic6—21no—
549Dic6—24no—
550Dic6C22×C3×C412yes—
551Dic6C22×C3×C412yes—
552C3×C8—21no—
553C3×C8—21no—
554C3×C8—22no—
555C3×C8—32no—
556C3×C8—41no—
557C3×C8—61no—
558C3×C8C2×C4×D312yes—
559C3×C8C22×C3×C412yes—
560C3⋊C8—21no—
561C3⋊C8C22×C3×C412yes—
562C2×C32—42no—
563C2×C32C2×C4×D411yescharacteristic
564C2×C32#57711yescharacteristic
565C2×C32#57811yescharacteristic
566C3×D3—22no—
567#41—34no—
568#41—62no—
569C2×Q8—34no—
570C2×Q8—31no—
571C2×Q8—31no—
572C2×Q8—61no—
573C2×Q8—62no—
574C2×Q8C22×C3×D311yescharacteristic
575C2×D4—61no—
576C2×D4C22×C3×D311yescharacteristic
577C22×C4—21no—
578C22×C4—31no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583Q16—34no—
584Q16—34no—
585SD16—34no—
586SD16C3×C4×D314yescomplemented
587M16—34no—
588C2×C8—31no—
589C2×C8—31no—
590C2×C8—62no—
591C2×C8C22×C3×D311yescharacteristic
592C2×C8C22×C3×D311yescharacteristic
593C4⋊C4—21no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4C22×C3×D311yescharacteristic
605C4⋊C4C22×C3×D311yescharacteristic
606C22⋊C4—21no—
607C22⋊C4—31no—
608C22⋊C4—31no—
609C22⋊C4—61no—
610C22⋊C4—61no—
611C42—21no—
612C42—31no—
613C42—61no—
614C42—61no—
615C42—61no—
616C42—61no—
617C42—61no—
618C42—61no—
619C42C22×C3×D311yescharacteristic
620C22×C3—22no—
621C22×C3—22no—
622C22×C3—21no—
623C22×C3—32no—
624C22×C3—42no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3—81no—
632C22×C3—81no—
633C22×C3C2×D3×D411yescharacteristic
634C22×C3C22×C3×D411yescharacteristic
635C2×D3—21no—
636C2×D3—21no—
637C2×D3C3×C4×D412yes—
638C3×C4—22no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—22no—
644C3×C4—22no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—32no—
648C3×C4—41no—
649C3×C4—42no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—61no—
655C3×C4—61no—
656C3×C4—62no—
657C3×C4—62no—
658C3×C4—81no—
659C3×C4—81no—
660C3×C4—121no—
661C3×C4—121no—
662C3×C4C22×C4×D311yescharacteristic
663C3×C4D3×#4111yescharacteristic
664C3×C4C23×C3×C411yescharacteristic
665C3×C4C2×C3×#4111yescharacteristic
666Dic3—21no—
667Dic3—21no—
668Dic3—22no—
669Dic3—22no—
670Dic3—41no—
671Dic3—41no—
672Dic3C3×C4×D412yes—
673C32#294711yescharacteristic, complemented, Sylow
674C23—21no—
675C23—31no—
676Q8—21no—
677Q8—32no—
678Q8—32no—
679Q8—64no—
680Q8—61no—
681Q8—61no—
682Q8C2×C3×C4×D312yes—
683D4—21no—
684D4—64no—
685D4C2×C3×C4×D312yes—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—31no—
690C2×C4—32no—
691C2×C4—32no—
692C2×C4—31no—
693C2×C4—31no—
694C2×C4—64no—
695C2×C4—64no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—81no—
701C2×C4—241no—
702C2×C4—241no—
703C2×C4C3×D3×D411yescharacteristic
704C2×C4C3×D3×D411yescharacteristic
705C2×C4C23×C3×D311yescharacteristic
706C8—21no—
707C8—32no—
708C8—61no—
709C8C2×C3×C4×D312yes—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—42no—
714C2×C3—42no—
715C2×C3—62no—
716C2×C3—82no—
717C2×C3C4×D3×D411yescharacteristic
718C2×C3#576211yescharacteristic
719C2×C3#577111yescharacteristic
720C2×C3C2×C3×C4×D411yescharacteristic
721C2×C3C3×#57711yescharacteristic
722C2×C3C3×#57811yescharacteristic
723D3—22no—
724C22—22no—
725C22—32no—
726C22—41no—
727C22—41no—
728C22—61no—
729C22—61no—
730C22C2×C3×D3×D411yescharacteristic
731C4—21no—
732C4—21no—
733C4—22no—
734C4—32no—
735C4—41no—
736C4—41no—
737C4—61no—
738C4—61no—
739C4—62no—
740C4—62no—
741C4—121no—
742C4—121no—
743C4C22×C3×C4×D311yescharacteristic
744C4C3×D3×#4111yescharacteristic
745C3—21no—
746C3#7964811yescharacteristic, direct product factor
747C3C3×#294711yescharacteristic, complemented
748C2—42no—
749C2—62no—
750C2C3×C4×D3×D411yescharacteristic
751C2C3×#576211yescharacteristic
752C2C3×#577111yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×C4×SD16C2
socleC22×C32C22×D4
prime radicalC2×C3×#237C22
cosocleC2×C3×C4C24×C3
hypercenterC3×C4×SD16D3
hypocenterC3C3×#2947
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4×SD16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C3×#5572C2semidirect
4. C32×C4×SD16C2semidirect
5. C3×#5164C2semidirect
6. C3×#5030C2semidirect
7. C3×#5018C2semidirect
8. C3×#4861C2semidirect
9. C3×#4853C2semidirect
10. C3×D3×#103C2semidirect
11. C3×#4790C2semidirect
13. C3×#4758C2semidirect
14. C3×C4×Dic12C2semidirect
15. C3×#4689C2semidirect
17. #79648C3direct (N × H)
29. C3×#915C4semidirect
66. #5572C2×C3semidirect
76. C3×C4×SD16D3semidirect
77. C3×C4×SD16C2×C3semidirect
82. #5164C2×C3semidirect
83. #5030C2×C3semidirect
84. #5018C2×C3semidirect
85. #4861C2×C3semidirect
86. #4853C2×C3semidirect
87. D3×#103C2×C3semidirect
88. #4790C2×C3semidirect
90. #4758C2×C3semidirect
91. C4×Dic12C2×C3semidirect
92. #4689C2×C3semidirect
100. C3×D3×Q8C2×C4semidirect
109. C32×SD16C2×C4semidirect
119. C3×#216C2×C4semidirect
120. C3×#214C2×C4semidirect
143. C3×Dic12C2×C4semidirect
144. C3×ΓL(1,𝔽25)C2×C4semidirect
189. #915C3×C4semidirect
288. C4×SD16C3×D3semidirect
319. D3×Q8C2×C3×C4semidirect
332. C3×SD16C4×D3semidirect
333. C3×SD16C2×C3×C4semidirect
384. #216C2×C3×C4semidirect
385. #214C2×C3×C4semidirect
408. Dic12C2×C3×C4semidirect
409. ΓL(1,𝔽25)C2×C3×C4semidirect
586. SD16C3×C4×D3semidirect
673. C32#2947semidirect
746. C3#79648direct (N × H)
747. C3C3×#2947semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3×#9152
C3×#55722
C3×#55462
C32×C4×SD162
C3×#51642
C3×#50302
C3×#50182
C3×#48612
C3×#48532
C3×D3×#1032
C3×#47902
C3×#47722
C3×#47582
C3×C4×Dic122
C3×#46892
C3×#29473
#796483